The Presentation of a Class of Orthogonal Vector-Valued Multivariate Wavelet Packets Associated with an Integer-Valued Dilation Matrix

The notion of vector-valued multiresolution analysis of space of vector-valued higher-dimensional functions is introduced. An approach for constructing orthogonal vector-valued higher-dimensional wavelet packets is presented and their properties are discussed by means of time-frequency analysis method, matrix theory and functional analysis method. Three orthogonality formulas concerning these wavelet packets are obtained. Finally, one new orthonormal bases of L²(R^p,C^r) are obtained by constructing a series of subspaces of orthogonal matrix-valued wavelet packets.